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Heliocentrism[edit]

Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work by Aristarchus in which he advanced the heliocentric model as an alternative hypothesis to geocentrism. Archimedes wrote:

You are now aware ['you' being King Gelon] that the "universe" is the name given by most astronomers to the sphere the center of which is the center of the earth, while its radius is equal to the straight line between the center of the sun and the center of the earth. This is the common account (τά γραφόμενα) as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the "universe" just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same center as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.[2]

Aristarchus suspected the stars were other suns[3] that are very far away, and that in consequence there was no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time.

It is a common misconception that the heliocentric view was rejected by the contemporaries of Aristarchus. This is due to Gilles Ménage's translation of a passage from Plutarch's On the Apparent Face in the Orb of the Moon. Plutarch reported that Cleanthes (a contemporary of Aristarchus and head of the Stoics) as a worshipper of the Sun and opponent to the heliocentric model, was jokingly told by Aristarchus that he should be charged with impiety. Gilles Ménage, shortly after the trials of Galileo and Giordano Bruno, amended an accusative (identifying the object of the verb) with a nominative (the subject of the sentence), and vice versa, so that the impiety accusation fell over the heliocentric sustainer. The resulting misconception of an isolated and persecuted Aristarchus is still transmitted today.[4][5]

Some facts suggest that Aristarchus' heliocentric model was an accepted theory for some centuries. It is known that a demonstration of the model was given by Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus,[6] but no full record has been found. Pliny the Elder[7] and Seneca[8] referred to planets' retrograde motion as an apparent (and not real) phenomenon, which is an implication of heliocentrism rather than geocentrism.

The heliocentric theory was successfully revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy with his three laws. Isaac Newton later gave a theoretical explanation based on laws of gravitational attraction and dynamics.

Distance to the Sun (lunar dichotomy)[edit]

Aristarchus's 3rd-century BC calculations on the relative sizes of (from left) the Sun, Earth and Moon, from a 10th-century AD Greek copy

The only surviving work usually attributed to Aristarchus, On the Sizes and Distances of the Sun and Moon, is based on a geocentric world view. It has historically been read as stating that the angle subtended by the Sun's diameter is 2 degrees, but Archimedes states in The Sand Reckoner that Aristarchus had a value of ½ degree, which is much closer to the actual average value of 32' or 0.53 degrees. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in Aristarchus' text.[9]

Aristarchus claimed that at half moon (first or last quarter moon), the angle between the Sun and Moon was 87°.[10] He might have proposed 87° as a lower bound, since gauging the lunar terminator's deviation from linearity to 1° accuracy is beyond the unaided human ocular limit (that limit being about 3° accuracy). Aristarchus is known to have also studied light and vision.[11]

Using correct geometry, but the insufficiently accurate 87° datum, Aristarchus concluded that the Sun was between 18 and 20 times farther away than the Moon.[12] (The true value of this angle is close to 89° 50', and the Sun's distance is actually about 400 times the Moon's.) The implicit false solar parallax of slightly under 3° was used by astronomers up to and including Tycho Brahe, c. AD 1600. Aristarchus pointed out that the Moon and Sun have nearly equal apparent angular sizes, and therefore their diameters must be in proportion to their distances from Earth; thus, the diameter of the Sun was calculated to be between 18 and 20 times the diameter of the Moon.[13]

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